Questions tagged [prior]
In Bayesian statistics a prior distribution formalizes information or knowledge (often subjective), available before a sample is seen, in the form of a probability distribution. A distribution with large spread is used when little is known about the parameter(s), while a more narrow prior distribution represents a greater degree of information.
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How to choose default uninformative prior in the R Package BAS
I'm conducting a Bayesian multilevel logistic regression based on the Rpackage BAS. I'm a beginner in Bayesian statistics.
But in bas.glm, I don't understand and I don't know how to specify my prior. ...
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What are the implications of setting off-diagonal elements of estimated covariance to 0?
I have sometimes seen in published work that when estimating covariance matrices, off-diagonal elements are set to 0. For example, in this paper, $N$ neurons are recorded and authors wish to use the $...
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how can predictive distributions be considered as expectations?
I guess that the prior and posterior predictive distributions can be considered expectation of $p(y|\theta )$ (in case of prior predictive distribution) and $p(\widetilde{y}|\theta )$ (in case of ...
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How to obtain likelihood ($P(B/R)$ given the prior $P(R)$ and the posterior $P(R/B)$
I am working on a topic related to multiple-choice response. I would like to measure the efficiency of the information source (or a student’s information search) and I believe Bayesian statistics is ...
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Can I use the Mean Squared Prediction Error to select the prior SD in a CausalImpact model?
I'm using the CausalImpact package (in R), and (as I expect is typical) the findings are very sensitive to the prior being used.
I have an OK understanding, I think, of what the prior is doing in this ...
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Estimating Markov Chain Probabilities with Limited Data
Suppose I have some data on transitions between states of a Discrete Time Markov Chain. Let's say that transitions between some events are observed more frequently from others. For example, in a 3 ...
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Does the example given correspond to a prior predictive check?
Could someone explain to me precisely what is meant by prior predictive check, in Bayesian inference? In some documents, one uses observed data (“in which we ...
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How to decide the parameters of a Gamma distribution for a Gamma-Poisson model?
In Bayesian inference, the Gamma-Poisson model uses usually a Gamma($\alpha$,$\beta$) prior on the $\lambda$ parameter of the Poisson distribution.
Are there any rules for setting appropriate values ...
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Strange Variance Term for Normal Prior $w^2\sigma^2$
I've attached two screenshots, one with the question and one with the answer. It seems to me that the prior is wrong and it should include $w^2$ not $w^2\sigma^2$
I apologise for, including such a ...
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How to choose between gamma and Gaussian given a choice of gauges?
I'm trying to make the choice between the gamma and Gaussian distributions as a prior distribution for some data. When I learned statistics a while ago, I was given the rule of thumb: if your data ...
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BIC with non-negligible priors
I want to do model selection based on the best-fit/MAP/marginal posterior I find from an MCMC and likelihood maximization. I have a likelihood $\mathcal{L}(X|\theta)$, some informative priors $\pi(\...
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Understanding PRIOR option in SCORE statement for PROC LOGISTIC (SAS)
Say I have a binary response which I want to model with logistic regression on covariates $x$. Fitting a model with PROC LOGISTIC will fit MLE coefficients for the model
$$
\text{logit}(\pi) = \alpha +...
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Avoid singular fits in mixed models in R with blme - checking layman's priors
While fitting linear mixed models, I would like to avoid zero random-effects (ranef(model)) and cluster-level SD estimates (...
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Turning a list of cost into categorical probability mass distribution
Background
Given a noisy dataset $D$, I have to solve a classification problem where the possible anserwer is $i\in\{1,\dots,N\}$. So far I can get pretty decent result with an algorithm that, based ...
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How should uncertainties be treated when scaling data for optimisation
I have a large dataset for which I am using Bayesian statistics for parameter estimation and model selection (using MultiNest for more detail).
This involves setting a prior over which the nested ...
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How is data generated when using an improper prior
Let $X$ be an $\mathcal{X}$ valued random variable. We are doing Bayesian statistics. Suppose that $\theta$ is a $\Theta$ valued random variable with known prior distribution $\Pi$ and that the ...
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Can we solve by hand the early exit multi-class classification problem? [closed]
Problem: Find a solution $\hat{\varepsilon}$ of the following minimization problem
\begin{align*}
&\min_{\varepsilon \in \mathbb{R}^M} \sum_{h=1}^M \varepsilon^h \hat{R}^h+\beta \sum_{h=1}^M \...
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Random sequence generator algorithm non informative piror distribution
I want to conduct a Bayesian statistical analysis of a sequence generation phenomenon.
The sequences generated contain elements from a known alphabet.
Working on that, I have tried to define the prior ...
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How to interpret a noninformative joint prior?
I am currently working on a homework assignment and have the following question:
$\theta_1$ and $\theta_2$ are parameters of interest and $y_1$ and $y_2$ are the likelihood functions which are $\text{...
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How to derive conditional destribution of MVN variable
I am working with following model specifications (Regression_ Modelle, Methoden und Anwendungen-Springer-Verlag Berlin Heidelberg (2009), p. 147):
$$Y \sim MVN(X\beta, \sigma^2I)$$
$$\beta|\sigma^2 \...
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Full conditional posteriors
so up to now I dealt with posteriors in the form of:
$$p(\theta|x) \propto p(x|\theta) p(\theta)$$
No we started to model a linear regression with the bayesian approach:
$$Y \sim MVN(X\beta, \sigma^2I)...
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How to sample from the prior predictive distribution with the BSTS R package?
Assuming I have to use the bsts package in R, I'm trying to understand the degree to which my prior distribution choices (implicit or otherwise) are consistent with ...
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Credible intervals with parameter near boundary
When doing Bayesian inference on a parameter that is bounded, often we use priors that approach 0 as the parameter approaches the boundary. For example, when estimating $(\mu, \sigma^2)$ for normal ...
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How to select a proper prior to control the time dependent structure of variable?
I am new in analyzing RCT data and not familiar with the techniques that are always used in RCT analysis.
I am analyzing a dataset of a study: An RCT study with 50 participants; the data was collected ...
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Do we ever use the prior predictive distributions of Bayesian Statistics?
As my question states, I am wondering if there is any chance we use the prior predictive distribution. I am studying Bayesian Statistics and have understood what it is. It is a must to go through in ...
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Understanding the Binomial likelihood notation
Let $X \sim Bin(n,\pi)$.
I don't understand why the binomial likelihood is then given by $f(x|\theta)=\binom{n}{x} \theta^x (1-\theta)^{n-x}$. Shouldn't it be $B(x|\pi,n)=P(X=k)=\binom{n}{k} \pi^k (1-\...
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Bayesian linear regression: How to enforce constraint on the sum of coefficients?
I have a linear regression problem in which my $X$ matrix is not full rank. Here is a small example:
$$X =
\left[\begin{array}{rrrr}
-1 & 0 & 0 & 1 \\
1 & 0 & -1 & 0 \\
0 &...
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Trouble understanding priors
The following comes from a book called Bayesian Statistics by Ben Lambert:
Assuming the following model for $r$ disease-positive people out of $n$ people:
$$Pr(Z=r, \theta) = {n\choose r}\theta^r(1-\...
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Choosing Bayesian Priors [duplicate]
I am fairly new to Bayesian Modeling, however I am experimenting with such framework in order to produce several estimates.
The part I am struggling the most with is the selection of prior ...
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How subjective are prior beliefs?
I find the term 'prior-beliefs' to be a little bit vague, what is acceptable to class as a prior belief in Bayesian analysis? For example, I could not look at any data and decide to myself "I ...
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